(Name, Address and Telephone Number of PersonAuthorized to Receive Notices and Communications)

September 25, 2018

(Date of Event Which Requires Filing of This Statement)

If the filing person has previously
filed a statement on Schedule 13G to report the acquisition which is the subject of this Schedule 13D, and is filing
this schedule because of §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box. ¨

NOTE: Schedules filed in paper format shall include a signed
original and five copies of the schedule, including all exhibits. See § 13d-7(b) for other parties to whom copies
are to be sent.

* The remainder of this cover page shall be filled out for a
reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment
containing information which would alter the disclosures provided in a prior cover page.

The information required on the remainder of this cover page
shall not be deemed to be “filed” for purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”)
or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however,
see the Notes).

CUSIP No.: 31189P102

1.

NAME OF REPORTING PERSON

Redmile Group, LLC

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

(a) ¨

(b) ¨

3.

SEC USE ONLY

4.

SOURCE OF FUNDS (SEE INSTRUCTIONS)

OO (1)

5.

CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) OR 2(e)

(1) The source of funds was working
capital of the Redmile Affiliates (as defined in footnote (2) below).

(2) The aggregate amount of shares of common
stock, $0.001 par value per share, of the Issuer (the “Common Stock”) that may be deemed beneficially owned
by the Reporting Persons is comprised of the following: (i) 525,459 shares of Common Stock held by Redmile Capital Fund, L.P.,
(ii) 1,954,210 shares of Common Stock held by Redmile Capital Offshore Fund, Ltd., (iii) 117,454 shares of Common Stock held by
Redmile Capital Offshore Fund (ERISA), Ltd., (iv) 2,384,128 shares of Common Stock held by Redmile Capital Offshore Fund II, Ltd.,
(v) 1,796,609 shares of Common Stock held by Redmile Strategic Master Fund, LP, (vi) 1,931,216 shares of Common Stock held by Redmile
Biopharma Investments I, L.P., (vii) 216,697 shares of Common Stock held by P Redmile Ltd., (viii) 202,593 shares of Common Stock
held by Map 20 Segregated Portfolio, a segregated portfolio of LMA SPC, and (ix) 1,231,300 shares of Common Stock held by a separately
managed account. Redmile Group, LLC is the investment manager/adviser to each of the private investment vehicles and separately
managed accounts listed in items (i) through (ix) (collectively, the “Redmile Affiliates”) and, in such capacity,
exercises sole voting and investment power over all of the shares held by the Redmile Affiliates and may be deemed to be the beneficial
owner of these shares. Jeremy C. Green serves as the managing member of Redmile Group, LLC and also may be deemed to be the beneficial
owner of these shares. Redmile Group, LLC and Mr. Green each disclaim beneficial ownership of these shares, except to the extent
of its or his pecuniary interest in such shares, if any.

Subject to the Beneficial Ownership Blocker
(as defined below), the Reporting Persons may also be deemed to beneficially own shares of Common Stock issuable upon conversion
of the following: (i) 223,663 shares of the Issuer’s non-voting Class A Convertible Preferred Stock (“Class A Preferred
Stock”) held by Redmile Capital Fund, L.P., (ii) 302,862 shares of Class A Preferred Stock held by Redmile Capital Offshore
Fund, Ltd., (iii) 33,441 shares of Class A Preferred Stock held by Redmile Capital Offshore Fund (ERISA), Ltd., (iv) 1,712,110
shares of Class A Preferred Stock held by Redmile Capital Offshore Fund II, Ltd., (v) 55,747 shares of Class A Preferred Stock
held by Redmile Strategic Master Fund, LP, (vi) 342,422 shares of Class A Preferred Stock held by Redmile Biopharma Investments
I, L.P., (vii) 30,121 shares of Class A Preferred Stock held by P Redmile Ltd., and (viii) 119,183 shares of the Class A Preferred
Stock held by Map 20 Segregated Portfolio, a segregated portfolio of LMA SPC. The Class A Preferred Stock is initially convertible
into shares of Common Stock on a one-for-five basis. Pursuant to the Certificate of Designation of Preferences, Rights and Limitations
of Class A Convertible Preferred Stock (the “Certificate of Designation”), the Issuer may not effect any conversion
of the Class A Preferred Stock, and a holder of the Class A Preferred Stock does not have the right to convert any portion of the
Class A Preferred Stock held by such holder, to the extent that, after giving effect to the attempted conversion set forth in a
notice of conversion, such holder, together with such holder’s affiliates and any other person whose beneficial ownership
of Common Stock would be aggregated with such holder’s for purposes of Section 13(d) or Section 16 of the Securities Exchange
Act of 1934, as amended (the “Exchange Act”), and the applicable regulations of the Securities and Exchange
Commission (the “SEC”), including any “group” of which such holder is a member, would beneficially
own a number of shares of Common Stock in excess of the Beneficial Ownership Limitation (the “Beneficial Ownership Blocker”).
The “Beneficial Ownership Limitation” is 9.99% of the shares of Common Stock then issued and outstanding, which
percentage may be changed at a holder’s election upon 61 days’ notice to the Issuer. Because the percentage of shares
of Common Stock collectively held directly by the Redmile Affiliates currently exceeds 9.99%, the conversion of the Class A Preferred
Stock held by the Redmile Affiliates is currently limited in its entirety by the Beneficial Ownership Blocker and the Reporting
Persons therefore cannot be deemed to have beneficial ownership over any of the shares of Common Stock issuable upon conversion
of the Class A Preferred Stock and such shares have not been included in the aggregate amount of shares of Common Stock beneficially
owned as reported in the table above.

(3) Percent of class calculated based on:
(a) 53,419,189 shares of Common Stock issued and outstanding as of August 3, 2018, as reported by the Issuer in its Quarterly Report
on Form 10-Q for the fiscal period ended June 30, 2018 filed with the SEC on August 6, 2018 (the “Form 10-Q”),
plus (b) 10,648,149 shares of Common Stock issued by the Issuer in an underwritten public offering (the “Offering”),
including 1,388,889 shares of Common Stock that were issued pursuant to the full exercise of the underwriters’ option to
purchase additional shares.

- 3 -

CUSIP No.: 31189P102

1.

NAME OF REPORTING PERSON

Jeremy C. Green

2.

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

(a) ¨

(b) ¨

3.

SEC USE ONLY

4.

SOURCE OF FUNDS (SEE INSTRUCTIONS)

OO (1)

5.

CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) OR 2(e)

(1) The source of funds was working capital
of the Redmile Affiliates.

(2) The aggregate amount of shares of Common
Stock that may be deemed beneficially owned by the Reporting Persons is comprised of the following: (i) 525,459 shares of Common
Stock held by Redmile Capital Fund, L.P., (ii) 1,954,210 shares of Common Stock held by Redmile Capital Offshore Fund, Ltd., (iii)
117,454 shares of Common Stock held by Redmile Capital Offshore Fund (ERISA), Ltd., (iv) 2,384,128 shares of Common Stock held
by Redmile Capital Offshore Fund II, Ltd., (v) 1,796,609 shares of Common Stock held by Redmile Strategic Master Fund, LP, (vi)
1,931,216 shares of Common Stock held by Redmile Biopharma Investments I, L.P., (vii) 216,697 shares of Common Stock held by P
Redmile Ltd., (viii) 202,593 shares of Common Stock held by Map 20 Segregated Portfolio, a segregated portfolio of LMA SPC, and
(ix) 1,231,300 shares of Common Stock held by a separately managed account. Redmile Group, LLC is the investment manager/adviser
to each of the Redmile Affiliates and, in such capacity, exercises sole voting and investment power over all of the shares held
by the Redmile Affiliates and may be deemed to be the beneficial owner of these shares. Jeremy C. Green serves as the managing
member of Redmile Group, LLC and also may be deemed to be the beneficial owner of these shares. Redmile Group, LLC and Mr. Green
each disclaim beneficial ownership of these shares, except to the extent of its or his pecuniary interest in such shares, if any.

Subject to the Beneficial Ownership Blocker,
the Reporting Persons may also be deemed to beneficially own shares of Common Stock issuable upon conversion of the following:
(i) 223,663 shares of Class A Preferred Stock held by Redmile Capital Fund, L.P., (ii) 302,862 shares of Class A Preferred Stock
held by Redmile Capital Offshore Fund, Ltd., (iii) 33,441 shares of Class A Preferred Stock held by Redmile Capital Offshore Fund
(ERISA), Ltd., (iv) 1,712,110 shares of Class A Preferred Stock held by Redmile Capital Offshore Fund II, Ltd., (v) 55,747 shares
of Class A Preferred Stock held by Redmile Strategic Master Fund, LP, (vi) 342,422 shares of Class A Preferred Stock held by Redmile
Biopharma Investments I, L.P., (vii) 30,121 shares of Class A Preferred Stock held by P Redmile Ltd., and (viii) 119,183 shares
of the Class A Preferred Stock held by Map 20 Segregated Portfolio, a segregated portfolio of LMA SPC. The Class A Preferred Stock
is initially convertible into shares of Common Stock on a one-for-five basis. Pursuant to the Certificate of Designation, the Issuer
may not effect any conversion of the Class A Preferred Stock, and a holder of the Class A Preferred Stock does not have the right
to convert any portion of the Class A Preferred Stock held by such holder, if the Beneficial Ownership Blocker applies. Because
the percentage of shares of Common Stock collectively held directly by the Redmile Affiliates currently exceeds 9.99%, the conversion
of the Class A Preferred Stock held by the Redmile Affiliates is currently limited in its entirety by the Beneficial Ownership
Blocker and the Reporting Persons therefore cannot be deemed to have beneficial ownership over any of the shares of Common Stock
issuable upon conversion of the Class A Preferred Stock and such shares have not been included in the aggregate amount of shares
of Common Stock beneficially owned as reported in the table above.

(3) Percent of class calculated based on:
(a) 53,419,189 shares of Common Stock issued and outstanding as of August 3, 2018, as reported by the Issuer on the Form 10-Q,
plus (b) 10,648,149 shares of Common Stock issued in the Offering.

- 5 -

This amendment No. 1 to Schedule 13D (this
“Amendment No. 1”) amends and supplements the Schedule 13D filed with the SEC on August 2, 2018 (the “Original
Schedule 13D”), by Redmile Group, LLC, a Delaware limited liability company (“Redmile”), and Jeremy
C. Green, a citizen of the United Kingdom (together with Redmile, the “Reporting Persons”) relating to the Common
Stock of Fate Therapeutics, Inc., a Delaware corporation (the “Issuer”).

ITEM 5.

Interest in Securities of the Issuer.

Item 5(a) of the Original Schedule 13D
is hereby amended and restated to read in its entirety as follows:

(a) The aggregate amount of shares of Common
Stock that may be deemed beneficially owned by the Reporting Persons is comprised of the following: (i) 525,459 shares of Common
Stock held by Redmile Capital Fund, L.P., (ii) 1,954,210 shares of Common Stock held by Redmile Capital Offshore Fund, Ltd., (iii)
117,454 shares of Common Stock held by Redmile Capital Offshore Fund (ERISA), Ltd., (iv) 2,384,128 shares of Common Stock held
by Redmile Capital Offshore Fund II, Ltd., (v) 1,796,609 shares of Common Stock held by Redmile Strategic Master Fund, LP, (vi)
1,931,216 shares of Common Stock held by Redmile Biopharma Investments I, L.P., (vii) 216,697 shares of Common Stock held by P
Redmile Ltd., (viii) 202,593 shares of Common Stock held by Map 20 Segregated Portfolio, a segregated portfolio of LMA SPC, and
(ix) 1,231,300 shares of Common Stock held by a separately managed account. Redmile Group, LLC is the investment manager/adviser
to each of the private investment vehicles and separately managed accounts listed in items (i) through (ix) (collectively, the
“Redmile Affiliates”) and, in such capacity, exercises sole voting and investment power over all of the shares
held by the Redmile Affiliates and may be deemed to be the beneficial owner of these shares. Jeremy C. Green serves as the managing
member of Redmile Group, LLC and also may be deemed to be the beneficial owner of these shares. Redmile Group, LLC and Mr. Green
each disclaim beneficial ownership of these shares, except to the extent of its or his pecuniary interest in such shares, if any.

Subject to the Beneficial Ownership Blocker
(as defined below), the Reporting Persons may also be deemed to beneficially own shares of Common Stock issuable upon conversion
of the following: (i) 223,663 shares of the Issuer’s non-voting Class A Convertible Preferred Stock (“Class A Preferred
Stock”) held by Redmile Capital Fund, L.P., (ii) 302,862 shares of Class A Preferred Stock held by Redmile Capital Offshore
Fund, Ltd., (iii) 33,441 shares of Class A Preferred Stock held by Redmile Capital Offshore Fund (ERISA), Ltd., (iv) 1,712,110
shares of Class A Preferred Stock held by Redmile Capital Offshore Fund II, Ltd., (v) 55,747 shares of Class A Preferred Stock
held by Redmile Strategic Master Fund, LP, (vi) 342,422 shares of Class A Preferred Stock held by Redmile Biopharma Investments
I, L.P., (vii) 30,121 shares of Class A Preferred Stock held by P Redmile Ltd., and (viii) 119,183 shares of the Class A Preferred
Stock held by Map 20 Segregated Portfolio, a segregated portfolio of LMA SPC. The Class A Preferred Stock is initially convertible
into shares of Common Stock on a one-for-five basis. Pursuant to the Certificate of Designation of Preferences, Rights and Limitations
of Class A Convertible Preferred Stock (the “Certificate of Designation”), the Issuer may not effect any conversion
of the Class A Preferred Stock, and a holder of the Class A Preferred Stock does not have the right to convert any portion of the
Class A Preferred Stock held by such holder, to the extent that, after giving effect to the attempted conversion set forth in a
notice of conversion, such holder, together with such holder’s affiliates and any other person whose beneficial ownership
of Common Stock would be aggregated with such holder’s for purposes of Section 13(d) or Section 16 of the Exchange Act and
the applicable regulations of the Securities and Exchange Commission (the “SEC”), including any “group”
of which such holder is a member, would beneficially own a number of shares of Common Stock in excess of the Beneficial Ownership
Limitation (the “Beneficial Ownership Blocker”). The “Beneficial Ownership Limitation” is
9.99% of the shares of Common Stock then issued and outstanding, which percentage may be changed at a holder’s election upon
61 days’ notice to the Issuer. Because the percentage of shares of Common Stock collectively held directly by the Redmile
Affiliates currently exceeds 9.99%, the conversion of the Class A Preferred Stock held by the Redmile Affiliates is currently limited
in its entirety by the Beneficial Ownership Blocker and the Reporting Persons therefore cannot be deemed to have beneficial ownership
over any of the shares of Common Stock issuable upon conversion of the Class A Preferred Stock and such shares have not been included
in the aggregate amount of shares of Common Stock beneficially owned as reported in Section 4(b) below.

For purposes of this Schedule 13D, the
percent of class was calculated based: (a) 53,419,189 shares of Common Stock issued and outstanding as of August 3, 2018, as reported
by the Issuer in its Quarterly Report on Form 10-Q for the fiscal period ended June 30, 2018 filed with the SEC on August 6, 2018
(the “Form 10-Q”), plus (b) 10,648,149 shares of Common Stock issued by the Issuer in an underwritten public
offering (the “Offering”), including 1,388,889 shares of Common Stock that were issued pursuant to the full
exercise of the underwriters’ option to purchase additional shares.

- 6 -

Item 5(b) of the Original Schedule 13D
is hereby amended and restated to read in its entirety as follows:

(b) Redmile Group, LLC:

(1) Sole Voting Power: 0

(2) Shared Voting Power: 10,359,666

(3) Sole Dispositive Power: 0

(4) Shared Dispositive Power: 10,359,666

Jeremy C. Green:

(1) Sole Voting Power: 0

(2) Shared Voting Power: 10,359,666

(3) Sole Dispositive Power: 0

(4) Shared Dispositive Power: 10,359,666

ITEM 6.

Contracts, Arrangements, Understandings or Relationship with Respect to the Securities of the Issuer.

Item 6 of the Original Schedule 13D is
hereby amended and supplemented by adding the following paragraph immediately prior to the last paragraph of Item 6:

Public Offering

On September 25, 2018, the Redmile Affiliates
purchased an aggregate 3,703,704 shares of Common Stock at a price of $13.50 per share in the Issuer’s underwritten public
offering. Redmile Group, LLC is the investment manager/adviser to each of the Redmile Affiliates and, in such capacity, exercises
sole voting and investment power over all of the shares held by such vehicles and accounts and may be deemed to be the beneficial
owner of these shares. Jeremy C. Green serves as the managing member of Redmile Group, LLC and also may be deemed to be the beneficial
owner of these shares. Redmile Group, LLC and Mr. Green each disclaim beneficial ownership of these shares, except to the extent
of its or his pecuniary interest in such shares, if any.

- 7 -

SIGNATURE

After reasonable inquiry and to the best
of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.